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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Equivalence (measure theory) ： ウィキペディア英語版 Equivalence (measure theory) In mathematics, and specifically in measure theory, equivalence is a notion of two measures being qualitatively similar. Specifically, the two measures agree on which events have probability zero. ==Definition== Let (''X'', Σ) be a measurable space, and let ''μ'', ''ν'' : Σ → R be two signed measures. Then ''μ'' is said to be equivalent to ''ν'' if and only if each is absolutely continuous with respect to the other. In symbols: :$\backslash mu\; \backslash sim\; \backslash nu\; \backslash iff\; \backslash mu\; \backslash ll\; \backslash nu\; \backslash ll\; \backslash mu.$ Thus, any event ''A'' is a null event with respect to ''μ'', if and only if it is a null event with respect to ''ν'': $\backslash mu(A)\; =\; 0\; \backslash iff\; \backslash nu(A)\; =\; 0$ Equivalence of measures is an equivalence relation on the set of all measures Σ → R. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Equivalence (measure theory)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.